RD-E: 2202 Ditching using SPH

Units: mm, ms, KN, GPa, kg.

The impact of a triangular prism object on water is simulated and the results are compared qualitatively ², also using the experimental data obtained from the Politecnico di Milano. ¹

Figure 2. Problem Data

The impacting prism is modeled using shell elements with an average mesh size of 15 mm x 15 mm. To shorten the computation, it is made rigid with an accelerometer on the main node of the rigid body. Additional mass is added to the main node of the rigid body, so the total mass of the prism is 27 kg.

The water is modeled using SPH particles with a face-centered cubic mesh and smoothing length "ho" equal to 21 mm. Each SPH weighs m=2.61 g. The SPH particle mesh can be generated in HyperMesh using the SPH panel with a face-centered cubic pitch=15, and a material density of 1.0e-6 $\raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$m{m}^3$}\right.$. HyperMesh will then automatically create SPH property /PROP/SPH. This results in 222005 SPH elements. The size of the water is adapted to the shape of the object to reduce the model’s size and the simulation’s CPU time. For an SPH analysis, air is not typically modeled.

Boundary Setup

An initial velocity of 11 m/s in the Z direction is defined on the main node of the rigid body of the prism. Gravity is also applied to the prism.

An outlet non-reflective boundary /SPH/INOUT, Ityp=3 is defined using a surface at a distance equal to 2 x h_o inside the SPH water elements. The surface is placed at a distance equal to 2 x h_o inside the water. The surface is shown in green in Figure 3 and is oriented so that its normal vector points inside the domain.

Figure 3. SPH Outlet Surface Non-reflective Frontiers (NRF) (green)

The fluid-structure contact between the impacting prism and SPH water is modeled using a /INTER/TYPE7 sliding penalty contact interface. The impacting prism is the main surface and the SPH elements are the secondary nodes. The contact thickness gap is defined as Gap_min=3. For situations when the contact thickness gap is important such as when the SPH particles are in a tank, define Gap_min=1/2 * (shell thickness + SPH diameter) or for solid elements Gap_min=1/2 * (SPH diameter).

The SPH particles are supported as MASS elements in HyperView. Their display type and size can be set in HyperView by using Preferences > Visualization. In this example, the animation results are directly output to an h3d file using the /H3D option. The pressure in the water can be plotted.

Figure 4 shows the variation in the pressure when the wedge ditches into the water at an impact velocity of 11 m/s.

Figure 4. Pressure results from a section cut

Output Acceleration

To measure the acceleration, an accelerometer is defined at the main node of the prism rigid body. The acceleration values were converted to g’s and compared to both the experimental values ¹ and the analytic solution proposed by Von Karman. ² The simulation acceleration is filtered using the same CFC 60 (-3db) filter frequency as the test data was filtered.

Figure 5. Deceleration of the prism for an impact velocity of 11 m/s

The SPH results are very close to the experimental test results and also to the analytical solution. The simulations show that the SPH approach using the OUTLET option /SPH/INOUT correctly models a vertical ditching event without any numerical problems.